Decisions Errors refer to the probability of making a wrong conclusion when doing hypothesis testing. When a researcher sets out to do a study, she typically has a hypothesis, or a prediction of what she thinks the results will be. She then conducts the study to find out whether her hypothesis is supported by data or not. Depending on the results of the study, she then makes a decision about his hypothesis. Of course, there is always the possibility of making a wrong conclusion, or committing a Decision Error.
There are two ways a researcher can make a Decision Error. She can either decide that his hypothesis is true when it is actually false, or decide that his hypothesis is false when it is in fact true.
For example, let's say you hypothesize that Psychology majors are poor in Math. In reality, Psychology majors are no better or worse in Math when compared to the general population of university students. But let's say for some reason, when you picked out your sample for your study, you ended up getting a lot of Psychology majors who were taking remedial Math classes. This leads you to conclude that your hypothesis is correct, and that Psychology majors are poor in Math, when in reality, you should have rejected your hypothesis. Thus, you are making a Decision Error.